When the loss fixes the maximum amount of indemnity, it is clear that the amount stated in the face of the policy cannot he taken as the measure of the real liability which a company assumes in insuring a piece of property. It is true that there is an abstract possibility that (-eery time a loss occurs it will he large enough to call for the full amount of the insurance; but there is a practical certainty that in many cases loss and indemnity will be less than the face of the policy. It is necessary, therefore, to calcu late what is the probable ratio of the indemnity to the amount of insurance, or. in other words. to estimate the probable intensity of the loss. This can he ascertained, not by a study of the char acteristics of the insured property, hut only by the statistical analysis of the results of past ex perience. If it were shown by such analysis that for any particular kind of property the in demnity in a large number of cases had been on the average one-half the amount stated in the face of the policy, then the amount the insurance company would actually have at stake in a policy issued on property of that kind would be one-half the amount stated in the face of the policy.
Degree of Probability.—The determination of the probability of the occurrence of the event against whose economic consequences insurance is granted is a much more complex matter than the determination of the amount which the in surance company has at stake on a given policy. It is evident that this probability will vary with the length of time for which the insurance is to be in force; that, other things being equal, the probability of the occurrence of a chance event is twice as great for two years as for one year_ It will he convenient to approach the problem by leaving out of consideration the element of time and assuming that all insurance is granted for a uniform period, say for one year. We may then eonsider what changes, if any. the introduc tion of the time element will involve.
It is to be noted in the first place that it is impossible to determine the degree of probability by the most exhaustive study of the individual risk. It is easy to see that there is more danger in one case than another; that, fur example. other things being equal. a wooden house likely to be burned than a stone- house, but what, the absolute probability is in either ease dues not appear. Whether either will be destroyed or not is a matter of chance', though with different degrees of probability. By this it is not meant. that the destruction is uncaused, but that the forces at work are so complex that human knowl edge is incapable of analyzing them completely.
As it is impossible to determine the degree of probability directly, the attempt is made to discover it in au indirect way. The method is the application of the theory of probability to the statistical results of past experience. The average of the pact is the probability of the fu ture. If the records show that for a series of years au event has occurred 10 times a year for every 10.000 opportunities for its occurrence, the degree of probability that it will occur in a fu ture year. conditions remaining unchanged. is denoted by the fraction 10 /10,000. or 1 IMO.
The actual number of occurrences in any one year may vary more or less from the probable number as indicated by the average. The prob able degree of this variation may be determined from the character of the past series. The greater the fluctuations in the series in the past. the greater the variations of actual from average that may he expected in the future. But what ever the character of the past series, it will always be true that increasing the number of opportunities, provided they an all alike, dimin ishes the probable variation of the actual num ber of occurrences in any future year from the probable number as determined by past experi ences. To state the same principle in a form inure directly applicable to insurance, the greater the number of similar risks included in a group, the smaller the i•ercentage of variation between the average number of losses for a series of years, and the actual number of losses for any particular year.
The influence of time on probability under these ideally simplified conditions, that is, on the hypothesis that all circumstances affecting the degree of danger remain unehanged. is ve ry simple. The probability varies directly in pro portion to the time. For n years the probability is n times as great as for one year. If, then, we represent by a the amount which an insurance company has at stake on a given policy. by p the probability of the occurrence of a loss within one year. and by n the number of years for which the eompany issues its policy. We should have the annual risk assumed by the company represented by the formula is y p, and the total risk for the n years represented by a y p Y. a.
The real difficulties involved in the attempt to estimate ri-k have not yet been touched upon. They are practical rather than theoretical. The determination of future events by the appliea tion of the theory of probabilities to the results of past experience proceeds on the basis of two assumptions; that all the cases included, whether past or future, are alike in all essential respects, and that the lapse of time brings no change in the factors affecting the degree of probability. Neither of these assumptions corresponds to the fact. As to the first we see that hardly any two lives or pieces of property are alike in all essential respects. In the case of fire insurance, for example, the number of circumstances affect ing the probability of destruction is very great. It is only by overlooking many minor points and assuming a degree of similarity that does not actually exist, that the application of the sta tistical method is at all possible. The same con siderations apply more or less to all other forms of insurance. The common practice is to group risks in classes, according to their more promi nent elements, and collect data about the differ ent classes from which to calculate the average. Each class has its own average and its own de gree of probability. In estimating an individual risk the average of the class to which it belongs is used as a basis from which the particular risk is calculated by making allowance for any special conditions affecting it. The result is at the best a more or less close approximation to reality.